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AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

Binomial Theorem MCQs - AP EAMCET

Binomial Theorem - AP EAMCET Mathematics

81. The binomial expansion of (1 + x)ⁿ where n is a positive integer is given by:
- A) ∑_k=0ⁿ ⇤ n_k x^k
- B) ∑_k=1ⁿ ⇤ n_k x^n-k
- C) ∑_k=0^n-1 ⇤ n_k x^k
- D) ∑_k=1^n-1 ⇤ n_k x^k
Answer: A
82. The middle term in the expansion of (a + b)⁶ is:
- A) 15a³b³
- B) 10a³b³
- C) 20a²b⁴
- D) 12a²b⁴
Answer: B
83. The binomial expansion of (1 + x)^1/2 up to the second term is:
- A) 1 + 1/2x
- B) 1 + 1/2x + 1/8x²
- C) 1 + x + 1/2x²
- D) 1 + x + 1/2x
Answer: B
84. The general term in the binomial expansion of (1 + x)ⁿ is:
- A) ⇤ n_r x^n-r
- B) ⇤ n_r x^r
- C) ⇤ n_r x^r * rⁿ
- D) ⇤ r_n x^n-r
Answer: B
85. What is the sum of the coefficients in the binomial expansion of (1 + x)⁷?
- A) 7
- B) 128
- C) 1
- D) 256
Answer: D
86. In the binomial expansion of (1 + x)ⁿ, the coefficient of x³ is:
- A) ⇤ n₃
- B) ⇤ 3_n
- C) ⇤ 3₁
- D) ⇤ n₁
Answer: A
87. The binomial expansion of (1 + x)^3/2 up to the first two terms is:
- A) 1 + 3/2x
- B) 1 + 3/2x + 3/8x²
- C) 1 + x + 3/2x²
- D) 1 + 3/2x + 1/8x²
Answer: B
88. The term independent of x in the expansion of (x + 1/x)⁶ is:
- A) 6
- B) 15
- C) 20
- D) 10
Answer: D
89. In the expansion of (1 + x)ⁿ, the number of terms is:
- A) n + 1
- B) n - 1
- C) n
- D) 2n
Answer: A
90. Using the binomial theorem, the approximation for (1 + x)^1/3 for small x is:
- A) 1 + 1/3x
- B) 1 + 1/3x + 1/9x²
- C) 1 + x + 1/2x²
- D) 1 + 1/3x + 1/27x²
Answer: A

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AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

Binomial Theorem - AP EAMCET Mathematics

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